Question

The number of solutions of log2(x – 1) = 2 log2(x – 3) is

• (A) 2
• (B) 1
• (C) 6
• (D) 7

Answer 1

The Correct Option is B

Explanation:
Given, ${\log }_2(x-1)=2{\log }_2(x-3)$$\Rightarrow {\log }_2(x-1)={\log }_2(x-3{)}^2$$\Rightarrow x-1=(x-3{)}^2$$\Rightarrow x-1=x^2+9-6x$$\Rightarrow x^2-7x+10=0$$\Rightarrow (x-2)(x-5)=0$$\Rightarrow x=2,5$since, $x=2$ does not satisfy the equation. So, $x=5$ is the only solution. Hence, number of solution is one.$x=2$ does not satisfy the equation as RHS becomes undefined.